Fundamental physical equations uniquely determined by their symmetry groups

AbstractChalcogenide semiconductors and glasses have many applications in the civil and military fields, especially in relation to their electronic, optical and mechanical properties for energy conversion and in enviormental materials. However, they are much less systemically studied and their fundamental physical properties for a large class chalcogenide semiconductors are rather scattered and incomplete. Here, we present a detailed study using well defined first-principles calculations on the electronic structure, interatomic bonding, optical, and mechanical properties for 99 bulk chalcogenides including thirteen of these crytals which have never been calculated. Due to their unique composition and structures, these 99 bulk chalcogenides are divided into two main groups. The first group contains 54 quaternary crystals with the structure composition (A2BCQ4) (A = Ag, Cu; B = Zn, Cd, Hg, Mg, Sr, Ba; C = Si, Ge, Sn; Q = S, Se, Te), while the second group contains scattered ternary and quaternary chalcogenide crystals with a more diverse composition (AxByCzQn) (A = Ag, Cu, Ba, Cs, Li, Tl, K, Lu, Sr; B = Zn, Cd, Hg, Al, Ga, In, P, As, La, Lu, Pb, Cu, Ag; C = Si, Ge, Sn, As, Sb, Bi, Zr, Hf, Ga, In; Q = S, Se, Te; $$\hbox {x} = 1$$ x = 1 , 2, 3; $$\hbox {y} = 0$$ y = 0 , 1, 2, 5; $$\hbox {z} = 0$$ z = 0 , 1, 2 and $$\hbox {n} = 3$$ n = 3 , 4, 5, 6, 9). Moreover, the total bond order density (TBOD) is used as a single quantum mechanical metric to characterize the internal cohesion of these crystals enabling us to correlate them with the calculated properties, especially their mechanical properties. This work provides a very large database for bulk chalcogenides crucial for the future theoretical and experimental studies, opening opportunities for study the properties and potential application of a wide variety of chalcogenides.

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SYMMETRY GROUPS AND INVARIANT STATISTICAL TESTS FOR FAMILIES OF MULTIVARIATE GAUSSIAN DISTRIBUTIONS

Mathematical Statistics Theory and Applications ◽

10.1515/9783112319086-051 ◽

1987 ◽

pp. 335-338

Keyword(s):

Statistical Tests ◽

Symmetry Groups ◽

Gaussian Distributions ◽

Multivariate Gaussian

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Crystallography: Symmetry groups and group representations

EPJ Web of Conferences ◽

10.1051/epjconf/20122200006 ◽

2012 ◽

Vol 22 ◽

pp. 00006

Author(s):

B. Grenier ◽

R. Ballou

Keyword(s):

Symmetry Groups ◽

Group Representations

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Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

Journal of High Energy Physics ◽

10.1007/jhep05(2021)105 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Magdalena Larfors ◽

Davide Passaro ◽

Robin Schneider

Keyword(s):

Line Bundle ◽

Complete Intersection ◽

Particle Physics ◽

Model Building ◽

Wilson Line ◽

Symmetry Groups ◽

The Standard Model ◽

Order Of Magnitude ◽

Systematic Program ◽

Calabi Yau Manifolds

Abstract The systematic program of heterotic line bundle model building has resulted in a wealth of standard-like models (SLM) for particle physics. In this paper, we continue this work in the setting of generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in ref. [1], we identify two geometries that, when combined with line bundle sums, are directly suitable for heterotic GUT models. We then show that these gCICYs admit freely acting ℤ2 symmetry groups, and are thus amenable to Wilson line breaking of the GUT gauge group to that of the standard model. We proceed to a systematic scan over line bundle sums over these geometries, that result in 99 and 33 SLMs, respectively. For the first class of models, our results may be compared to line bundle models on homotopically equivalent Complete Intersection Calabi Yau manifolds. This shows that the number of realistic configurations is of the same order of magnitude.

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